The vacancy has attracted much speculation since incumbent Michael Grade announced he would be leaving ITV.
Sir Crispin Davis, former chief executive of Reed Elsevier, is believed to have withdraw from the process. This follows four other near-misses for the broadcaster as it desperately tries to stabilise its board.
In recent months Simon Fox, chief executive at HMV, Pascal Cagni, chief exectutive at Apple Europe, and former BSkyB chief executive Tony Ball have all been linked with the ITV role.
Bishop is also the former chairman of airline BMI. He was chairman of Channel 4 from 1993 to 1997, earning praise for his work at the broadcaster. He was central to Channel 4 remaining a public company while the Conservative Party was in power.
Earlier this year, Bishop sold his 50% stake in BMI to German carrier Lufthansa for £223m.
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